1. Field of the Invention
This invention relates to a method of generating a complex curved surface and, more particularly, to a method of generating a complex curved surface by combining at least two three-dimensional curved surfaces.
2. DESCRIPTION THE RELATED ART
A curved surface of a three-dimensional metal mold or the like on a design drawing is generally expressed by a plurality of section curves, but no profile data is shown for the shape of the area lying between a certain section curve and the next adjacent section curve. In numerically controlled machining it is essential that machining be carried out so as to smoothly connect these two section curves despite the fact that the profile between them is not given. In other words, this means that machining must be performed by generating the curved surface between the two section curves from such data as that indicative of the section curves, storing on an NC tape the data concerning the generated curved surface, and carrying out machining in accordance with commands from the NC tape. To this end, there has been developed and put into practical use a method comprising generating a plurality of intermediate sections in accordance with predetermined rules from data specifying several sections and section curves of a three-dimensional curved body, finding a section curve (intermediate section curve) on the curved body based on the intermediate sections, and generating a curved surface of the three-dimensional body based on the plurality of generated intermediate section curves. (For example, see U.S. Pat. No. 4,491,906). This method is useful in generating a smooth curved surface from section data.
Depending upon machining, there are cases where it is necessary to machine a complex curved surface obtained by combining two or more three-dimensional curved surfaces, or in other words, to create a complex curved surface. However, it is not possible with the prior art to create a complex curved surface in a simple manner by combining these three-dimensional curved surfaces using the data indicative of each three-dimensional curved surface. Accordingly, the applicant has proposed in Japanese Patent Application No. 60-39445 (corresponding to PCT/JP86/00100) a novel method of creating complex curved surfaces.
This proposed method of creating complex curved surfaces includes the following steps, with reference being had to FIG. 8:
(a) inputting data in advance for specifying first and second three-dimensional curved surfaces 12a, 12b constituting a complex curved surface 11;
(b) inputting data specifying one line of intersection CL.sub.i on a predetermined plane (e.g. the X-Y plane) 10 as well as a rule for specifying a number of lines of intersection on the X-Y plane on the basis of said line of intersection;
(c) finding first and second section curves 13a, 3b obtained when the first and second three-dimensional curved surfaces 12a, 12b are cut by a section which has the i-th line of intersection CL.sub.i, among the number of lines of intersection, as its line of intersection with the X-Y plane;
(d) obtaining a point of intersection CR.sub.i between the two section curves 13a, 13b; and
(e) generating the complex curved surface 11 by adopting a set of the points of intersection CR.sub.i (i=1, 2, . . . ) corresponding to the lines of intersection CL.sub.i (i =1, 2, . . . ) as an intersection CRL between the first and second three-dimensional curved surfaces 12a, 12b.
The section curves 13a, 13b are obtained as sets of discrete points on the respective three-dimensional curves surfaces 12a, 12b and the section curves 13a, 13b are specified by obtaining points over the entire range of these three-dimensional curved surfaces. In other words, for the first three-dimensional curved surface 12a, the section curve 13a is specified by discretely obtaining all points from the end point Al to the end point A2; for the second three-dimensional curved surface 12b the section curve 13b is specified by discretely obtaining all points from the end point B1 to the end point B2.
Thus, with the proposed method, the section curves 13a, 13b are obtained over the entire range (between A1 and A2 and between B1 and B2) of the respective three-dimensional curved surfaces, the point of intersection CR.sub.i is found by using the section curves obtained, and an intersection is formed by similarly obtaining a set of obtained points of intersection CR.sub.i (i=1, 2, . . . ).
However, the segment from CR.sub.i to end point A2 on the section curve 13a and the segment from CR.sub.i to end point B1 on the section curve 13b do not form a complex curved surface but are necessary merely for the purpose of obtaining the point of intersection CR.sub.i, which can be found even if section curves are not obtained over the entire ranges mentioned above.
In other words, a problem with the proposed method is that a considerable period of time is required for processing since unnecessary segments of the section curves are obtained.
Accordingly, an object of the present invention is to provide a complex curved surface creation method in which it suffices to obtain only section curves within predetermined ranges necessary for generating a complex curved surface, thereby shortening processing time.